Exploring the lower limit in hydrogen bonds: analysis of weak C-H...O and C-H...pi interactions in substituted coumarins from charge density analysis

Experimental electron densities in coumarin, 1-thiocoumarin, and 3-acetylcoumarin have been analyzed based on the X-ray diffraction data at 90 K. These compounds pack in the crystal lattice with weak C-H...O and C-H...pi interactions, and variations in charge density properties and derived local energy densities have been investigated in the regions of intermolecular interactions. Theoretical charge density calculations on crystals using the B3LYP/6-31G* method show remarkable agreement with the derived properties and energy densities from the experiment. The intermolecular interactions follow an exponential dependence of electron density and energy densities at the bond critical points. The Laplacian follows a "Morse-like" dependence on the length of the interaction line. Based on the set of criteria defined using the theory of "atoms in molecules", it has become possible to distinguish between a hydrogen bond (C-H...O) and a van der Waals interaction (C-H...pi). This has resulted in the identification of a "region of overlap" in terms of electron densities, energy densities, and mutual penetration of the hydrogen and acceptor atoms with respect to the interaction length. This approach suggests a possible tool to distinguish between the two types of interactions.     

Dipole moment enhancement in molecular crystals from X-ray diffraction data.

Although reliable determination of the molecular dipole moment from experimental charge density analyses on molecular crystals is a challenging undertaking, these values are becoming increasingly common experimental results. We collate all known experimental determinations and use this database to identify broad trends in the dipole moment enhancements implied by these measurements as well as outliers for which enhancements are pronounced. Compelling evidence emerges that molecular dipole moments from X-ray diffraction data can provide a wealth of information on the change in the molecular charge distribution that results from crystal formation. Most importantly, these experiments are unrivalled in their potential to provide this information in such detail and deserve to be exploited to a much greater extent. The considerable number of experimental determinations now available has enabled us to pinpoint those studies that merit further attention, either because they point unequivocally to a considerable enhancement in the crystal (of 50 % or more), or because the experimental determinations suggest enhancements of 100 % or more--much larger than independent theoretical estimates. In both cases further detailed experimental and theoretical studies are indicated.     

Exploring potent ligand for proteins: insights from knowledge-based scoring functions and molecular interaction energies

Structural Chemistry - Two different scoring functions, Hirshfeld fingerprint-based scoring (HFBS) and molecular operating environment (MOE), and the kernel energy method (KEM) along with...     

The circle method and bounds for L-functions - I

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi $ be a primitive character of conductor $M$ . For the twisted $L$ -function $L(s, f\otimes \chi )$ we establish the hybrid subconvex bound $$\begin{aligned} L\left( \frac{1}{2}+it, f\otimes \chi \right) \ll (M(3+|t|))^{\frac{1}{2}-\frac{1}{18}+\varepsilon }, \end{aligned}$$ for $t\in \mathbb{R }$ . The implied constant depends only on the form $f$ and $\varepsilon $ .     

Identification of a new co-crystal of salicylic acid and benzamide of pharmaceutical relevance

Raman spectroscopy, X-ray powder diffraction/X-ray crystallography and differential scanning calorimetry have been used to study the phenomenon of co-crystal formation in stoichiometric mixtures of salicylic acid with benzamide. Raman spectroscopy was particularly useful for the characterization of the products and was used to determine the nature of the interactions in the co-crystals. It was observed that little change in the vibrational modes associated with the phenyl groups of the respective reactants took place upon co-crystal formation, but changes in intensities of the vibrational modes associated with the amide and the carboxylic acid groups were observed upon co-crystal formation. Several new vibrational bands were identified in the co-crystal which were not manifested in the physical mixture of both components and could be used as diagnostic features of co-crystal formation.     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.     

Effect of colour singletness of quark-gluon plasma in quark-hadron phase transition

Consequences of the constraint of SU(3) colour singletness of quark-gluon plasma are studied. This restriction increases the free energy barrier for the formation of hadronic bubble in supercooled phase and influences significantly the dynamics of the initial stage of quark-hadron phase transition. It also introduces terms dependent on the volume occupied by the plasma in the energy density and the pressure. These modifactions vanish in the limit of an infinite volume. The last stage of the hadronization of the QGP likely to be formed in relativistic heavy ion collisions is necessarily characterized by a decreasing volume containing the quark matter, and thus these corrections become important. The nucleation of plasma droplets at AGS energies is also seen to be strongly affected by the requirement of colour singletness, and the choice of prefactor. Received: 4 December 1997 / Published online: 15 May 1998     

Inequalities for divisor functions

We give certain optimal inequalities for the divisor function. Such inequalities are useful in estimating the sums of divisor functions which are required in many standard arguments in analytic number theory.     

In situ formation of ruthenium catalysts for the homogeneous hydrogenation of carbon dioxide

A total of 44 different phosphines were tested, in combination with [RuCl(2)(C(6)H(6))](2) and three other Ru(II) precursors, for their ability to form active catalysts for the hydrogenation of CO(2) to formic acid. Half (22) of the ligands formed catalysts of significant activity, and only 6 resulted in very high rates of production of formic acid. These were PMe(3), PPhMe(2), dppm, dppe, and cis- and trans-Ph(2)PCH=CHPPh(2). The in situ catalysts prepared from [RuCl(2)(C(6)H(6))](2) and any of these 6 phosphine ligands were found to be at least as efficient as the isolated catalyst RuCl(O(2)CMe)(PMe(3))(4). There was no correlation between the basicity of monophosphines (PR(3)) and the activity of the catalysts formed from them. However, weakly basic diphosphines formed highly active catalysts only if their bite angles were small, while more strongly basic diphosphines had the opposite trend. In situ (31)P NMR spectroscopy showed that trans-Ru(H)(2)(dppm)(2), trans-RuCl(2)(dppm)(2), trans-RuHCl(dppm)(2), cis-Ru(H)(O(2)CH)(dppm)(2), and cis-Ru(O(2)CH)(2)(dppm)(2) are produced as the major metal-containing species in reactions of dppm with [RuCl(2)(C(6)H(6))](2) under catalytic conditions at 50 degrees C.     

Void-fraction reconstruction with stochastic data

The technique of computerized tomography has been used earlier to measure point density (or void-fraction) distribution in air-water flows. The interrogation source used in the measurement system was a gamma ray source, Cs-137. The inherent nature of such sources is the Poisson nature of the emmitted radiation. This Poisson corruption leads to imperfections in the projection data, i.e., the data no longer represents the line integral of the desired property being measured. The present study was conducted to assess the sensitivity of the tomographic reconstruction process to the statistical (Poisson) uncertainity in the projection data. Reconstruction experiments performed on six different sets of data indicate that influence of Poisson errors on reconstruction profiles is much more pronounced near the centre of the pipe in all the cases indicating the need for stronger gamma ray sources than the 13.6 milli-Curie used in the earlier investigations.On leave from: Indian Institute of Technology, Kanpur 208016, India